Question

Derive the formula for kinetic energy​

Answer 1

Answer:

1/2 mv^2

Explanation:

Expression for  Kinetic energy(Ek)-

Consider an object with mass m, moving with initial velocity u. Let a force F, act on it causing a displacement s, along the direction of force and accelaration. Let the object attain final velocity v.

We know F = m x a ------------------------ 1

By position velocity relation we have,

V2 = u2 + 2as

or s = v2 -u2 / 2a ----------------------------- 2

The work done by the force

W = F x s -------------------------------------- 3

Substituting 1 and 2 in 3

W = (m x a) x (v2 - u2/2a)

W = m/2 (v2 - u2)

W = 1/2 mv2 - 1/2 mu2 -------------------- 4

For an object to be at rest in the beggining, u = 0

Therefore, W = 1/2 mv2

W = Ek ( Ek = kinetic energy)

Therefore, Ek = 1/2 mv2

Answer 2

Answer:

Let us considered a body of mass 'm'moving with velocity 'v' having a displacement 's' . Also considered the body starting from rest and therefore the acceleration produced in the body is 'a'

${v}^{2} = {u}^{2} + 2as$

${v}^{2} = 2as...(as \: the \: u \: is \: 0).....eq.1$

if if a force 'f' acts on the body,

= f = ma

or , a =f /m ........eq.2

From eq.1 and eq.2

${v}^{2} = 2 \frac{ f}{m} \times s$

$2(f \times s) = m { v}^{2}$

$f \times s = \frac{ 1}{2} m {v}^{2}$

Therefore..

$w = \frac{1}{2} m {v}^{2} ......since \: w = f \\ \times s$

due to this work the object acquires the capacity of doing work.

therefore,

its its kinetic energy (k)= work done(w)=1/2mv^2

hope it will help please mark as brainliest.

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thus .... k = 1/2 mv^2